6.002 Spring 2018 Lecture 7 1

6.002 CIRCUITS ANDELECTRONICS

Lecture 7 – MOSFET, MOSFET amplifier

March 1, 2018

Contents:1. Review of amplifiers2. MOSFET i-v characteristics3. MOSFET amplifier4. Small signal response

Reading Assignment:Agarwal and Lang, Ch. 7 (��7.3-7.6)

Handouts:Lecture 7 notes

Announcements:• Quiz on 3/14 (Wed) at 7:30-9:30PM in 10-250

6.002 Spring 2018 Lecture 7 3

1. Review of amplifiers• Last time we studied this circuit:

• Transfer characteristics:

Circuit behaves as amplifier if: RLG>1

6.002 Spring 2018 Lecture 7 4

• Key device needed to make an amplifier: voltage-controlled current source

• Is there a device that exhibits this behavior? Yes! The MOSFET!

Ii

Iv

Oi

Ov+

–

+

–IGv

6.002 Spring 2018 Lecture 7 5

4. Transistors… The MOSFET• MOSFET=Metal-Oxide-Semiconductor

Field-Effect Transistor• MOSFET=three terminal semiconductor

device• In the MOSFET: Current through two

terminals (source and drain) controlled by voltage in third terminal (gate).

• Two different kinds: n-type and p-type• A modern microprocessor contains ~109-

5x109 MOSFETs

Inte

l 22

nm M

OS

FET

6.002 Spring 2018 Lecture 7 7

• i-v characteristics of 2N7000

Satur

ation

Linea

r

Cut-off

6.002 Spring 2018 Lecture 7 10

Three regimes of operation:– Cut-off: vGS ≤ VT

iD=0

– Linear or triode: vGS >VT, vDS ≤ vGS-VT

iD depends on vGS and vDS

– Saturation: vGS >VT, vDS ≥ vGS -VT

iD depends only on vGS

MOSFET i-v characteristics

6.002 Spring 2018 Lecture 7 11

• MOSFET as voltage-controlled current source:

• MOSFET as switch:

6.002 Spring 2018 Lecture 7 12

MOSFET equations

– Cut-off: vGS ≤ VT

– Linear or triode: vGS >VT, vDS ≤ vGS -VT

– Saturation: vGS >VT, vDS ≥ vGS –VT

Two parameters characterize the MOSFET in this simple model:– Threshold voltage: VT (in V)– �K factor�: K (in A/V2)

6.002 Spring 2018 Lecture 7 14

• Compare behavior of MOSFET in saturation with that of voltage-controlled current source:

• In MOSFET in saturation, the gate-source voltage is the control voltage.

• Key to make MOSFET amplifier: use MOSFET in saturation!

iO

vO

vI

I=GvI

00

6.002 Spring 2018 Lecture 7 15

3. MOSFET amplifier• In analogy with:

• Consider this circuit:

6.002 Spring 2018 Lecture 7 16

• How does it work?• Use graphical technique first:

àdraw �load line� associated with RL

• Operating point of amplifier at intersection of load line with MOSFET characteristics.

Vo=VS-RL.iD

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• Sketch the transfer characteristics:

• When MOSFET in saturation, transfer

characteristics steep à high voltage gain!

Vo=Vs-RL.iD

6.002 Spring 2018 Lecture 7 18

• High voltage gain region suitable for amplifier:

6.002 Spring 2018 Lecture 7 19

• Cutoff and linear regions unsuitable for amplifier: low gain and distortion

Demo

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• In saturation, MOSFET operates as current source à equivalent circuit:

How to quantitatively calculate transfer characteristic?

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• Amplifier transfer characteristics:

Node equation for node vO:

Then, transfer characteristics:

Note: transfer function is quadratic

à distortion!!

Demo

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4. How to minimize distortion: Small-signal• Transfer characteristics of MOSFET amp

are not linear:

à distortion!

• Key insight: if magnitude of signal is smallrelative to VS, transfer characteristics around bias point look fairly linearà low distortion.

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• If one can linearize, what are the vo-vismall-signal transfer characteristics?

• Large-signal transfer characteristics:

• Input is of form:

• Output should then be of form:

• Identify terms:

– Bias terms:

– Small-signal terms:

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• Small-signal terms:

• Linearizing means keeping only the linear term:

• Small-signal gain:

slope: -KRL(VI -VT)

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• When is this approximation good?

quadratic term << linear term

Or:

• The higher the bias, the easier it is to deliver this condition.

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• Let’s put some numbers: use 2N7000 (VT=2 V, K=0.14 A/V2)

with RL=250 Ω and VS=5 V.Transfer characteristics look like:

If select VO=2.7 V, then VI=2.4 V, and:

Input waveform with Vi=80 mV [≈0.2(VI –VT )], gives output waveform with Vo=1 V.

6.002 Spring 2018 Lecture 7 27

• More generally, obtain small-signal transfer characteristics by Taylor series expansion of large-signal transfer characteristics.

• If large-signal transfer characteristics are:

• Then, if vI=VI+vi, expand around (VI,VO):

• Small-signal transfer characteristics are:

• And small-signal gain is:

[check that from here, you get the same result as above]

6.002 Spring 2018 Lecture 7 28

Summary

• Three regimes of operation to a MOSFET: cutoff, linear and saturation

• In order to make an amplifier, MOSFET must be used in saturation

• A simple MOSFET model provides adequate description of i-v characteristics and requires only two parameters:– Threshold voltage– �K factor�

• An amplifier can be constructed with one MOSFET and one resistor.

• Transfer characteristics are quadratic (some degree of distortion introduced)